1. Field of the Invention
The present invention relates to the projection of principal and secondary features from the surface of an Earth globe or non-planar surface, such as a celestial sphere, spherical body and the like, with a practical minimum of distortion of those principal and secondary features. The principal features are projected onto identifiable panels which are suitable for individual study. The panels may then be assembled into a polyhedral approximation of the Earth globe or other celestial sphere, spherical body and the like and are therefore simultaneously useful in both their two and three dimensional forms.
2. Description of the Prior Art
It is fundamentally impossible to project without distortion a non-planar surface such as that of the Earth or other spherical body onto a flat surface. This is a mathematical truism. The curvature of a spherical body's surface can only be presented undistorted, that is, preserving areas, shapes and angles, when projected on another spherical body. Although such three-dimensional maps are inherently more accurate, they suffer the problem of being unwieldly and not very useful as training tools. There is no practical substitute for flat, two-dimensional maps, particularly in the educational process. Nor is there any other practical way to create maps which can be printed in atlases, text books and the like, and which can be given to students on inexpensive paper to work with while learning.
Accordingly, because of inconvenience of working with globes and other three-dimensional maps, and the advantages of having the entire surface of the Earth and other three-dimensional bodies projected onto a flat surface or surfaces, cartographers have long sought to develop means for projecting spherical surfaces onto flat pieces of paper with a minimum of distortion of the features therein. In 1989 the U.S. Geological Survey, Department of the Interior, published An album of Map Projections, Professional Paper 1453, in an effort to categorize the existing known projections. That publication states that there are literally hundreds of known projection systems. Until at least recently, the map most generally used in schools, textbooks and in the news media to represent the entire Earth has been the Mercator projection, devised in the sixteenth century. However, while the Mercator projection preserves angles and therefore is particularly useful for marine charts, it presents a misleading view of the world because of the excessive distortion of areas and distances as one proceeds farther from the equator. Thus, for example, the Mercator projection shows the size of Greenland nearly as large as the size of South America when in actuality it is only one-sixteenth the size of South America.
The National Geographic Society had for more than 50 years utilized the Van der Grinten Projection for its world maps, despite the excessive distortion contained therein, namely, for example, +258% for Canada, +68% for the U.S., +14% for South America, +223% for the U.S.S.R., 7% for Africa and +61% for China. In 1988 the National Geographic Society discontinued its use of the Van der Grinten projection and adopted the Robinson Projection in an effort to more accurately portray the areas of the principal features of Earth on flat surfaces. The Robinson Projection was developed in 1963 and reduces some of the distortion of Earth's land masses. However, while areas in the Robinson map are relatively correct, shapes far from the equator, such as Alaska, are stretched almost out of recognition. Nor does the Robinson projection provide a means for individually studying the major land masses of Earth and it cannot be assembled into a three-dimensional form.
The Dymaxion Map, copyrighted in 1982 by Buckminister Fuller Institute, projects the Earth globe onto 20 identical equilateral triangular segments and shows, with a minimum of distortion, all the land masses of Earth on a single flat sheet of paper. The sheet can be folded along the lines of its constituent triangles into an icosahedral three dimensional representation of the globe. However, the Dymaxion Map is not particularly useful for educational or even entertainment purposes. If broken apart into individual triangles, the land masses are cut into incoherent portions and, if not broken apart into individual triangles, the Dymaxion Map is ungainly when laid out flat in one piece and very hard to interpret as a map of continents and countries.
In C.D.B. Bryan's review of the National Geographic's first 100 years there is disclosed a picture of a polyhedral globe. The globe is a 24-faceted shell, each facet side having four edges and the identical "kite" shape. The Equator is a plurality of regular octagons running around the mid-point. However, National Geographic's 24 kite-shaped pieces chop most of the land masses to shreds when disassembled and is therefore only useful in its three-dimensional form.
Numerous other projections have been known in the art. U.S. Pat. No. 2,153,053 discloses a polyhedral approximation of the Earth globe having twelve regular pentagonal sides surrounding a collapsible frame. It is designed for school use. However, upon disassembly its land masses are cut.
U.S. Pat. No. 2,393,676 depicts a projected map having a plurality of square and triangular sections To facilitate cartographic construction, all edges are on great circles. One embodiment has six equilateral square sections and eight equilateral triangles.
None of the above described map making systems have achieved that combination of a two and three-dimensional map wherein distortion is kept to a minimum and principal features are easily studied in two-dimensional form.